/sci/ - Science & Math

>>9414912
looks fine to me, are you a brainlet?

>>9414912
Most math textbooks are equally bad. I think authors write to stroke their own egos. That or they are highly autistic

>>9414912
which book is that? it assumes familiarity with calculus-level basic DEs

>>9414918
fuck off. if you don't know any math and can't learn for some reason, don't post in math threads

>>9414921
I know math son. Just because I study it doesn't mean I agree there shouldn't be more words on a page in most math books. I could write something equally as bad in OP with nothing but terse symbols on a page in the prelim section of a book that has the words "Intro" in it. I could ensure 99% of the people reading it wouldn't understand everything (i.e. students), but what point would it serve?

>>9414912
>1st day definition of a 1st order system of DEs
>1st day trick to turn nth order equation into a coupled system of first order equations by introducing new variables for the derivatives and including equations setting them equal

You literally haven't done anything yet.

>>9414921
>it assumes familiarity with calculus-level basic DEs
I do know how to do those, not with vectors though
>>9414931
why can't he just explain it? I don't know what a coupled system

>>9414931
hindsight is 20/20. You already studied the material, but when you first learned it you were retarded too.

>>9414928
>>9414928
>I could
you couldn't do shit because you don't know any math. cut the nonsense and go away.

>>9414942
>but when you first learned it you were retarded too.
Speak for yourself.

>>9414912
What book is it? It's not any of the common intro ODEs books.

>>9414944
>>9414946
U is a retard tho. stop lyin

>>9414917
you probably already know ordinary diff eqs

>>9414949
"Ordinary Differential Equations" by Tenenbaum & Pollard
it's recommended on the /sci/ wiki and I saw it in this thread >>9410212 so I expected it to be good

>>9414953
the terminology tends to be all fucked up in math books for non mathematicians

this page isn't saying much. it's just defining things. e.g. the first line is defining what a system of d first order differential equations with an initial condition is (1.1)

I really like this book, helped me a lot during my PDEs course

>>9414912
thats a laplace transform I believe.

>>9414912

Jesus, that would be awful if it's supposed to be an intro book for someone not too used to reading math.

Looks like something a physishit would write to make it seem more difficult than it actually is.

>>9414980
To be fair. Most ODE text books suck apparently.

>>9414980
It's an issue many math books have due to the ego of their authors who instead of trying to make the subject palatable and understandable elect instead to jerk off by trying to show off their mad math skills and beautiful equations.

>>9414962

>>9414912
I haven't read it but its format looks disgusting and unreadable.

>>9414953

It's not. I have my copy right in front of me and that's not chapter 1. Chapter 1 Lesson 1 is about how differential equations originate using the half life of C14 as an example.

>>9414990
your post got deleted and you think it's valuable enough to post it again? your opinion is trash. fuck off.

>>9415007
Wait, what post got deleted?

>>9414912
I've yet to find a decent introduction to differential equations. What helped me most was just playing around with them in Mathematica. Once you get used to the mechanics of how they work on an intuitive level, the notation is secondary and you can pick up on the ideas themselves.

I'd recommend starting out by looking at systems of first order DIFFERENCE equations (the discrete-time analogue of differential equations), which are much more intuitive in the way they operate and why you might want to study them.

>>9415011
fuck off

>>9414953
Scroll to the top of the pdf and find out who the author really is.

>>9415021
A post I didn't post got deleted before I posted a post which was identical to the aforementioned post.

You have a lot of explaining to do.

>>9415021
>>9415035
Oh I see the thread now. It's almost saying the same thing, but not really.

Silly anon.

>>9414912
>you probably already know ordinary diff eqs

I learned that shit in highschool, brainlet kiddo.

>>9414998
I guess you're implying I am somewhere passed valley of despair because I am not wrong.

>>9415049
>passed
No, you're still in the valley.

>>9415055
thanks.

>>9415049
You are wrong, freshman retard. Laplace transform is nowhere on that page.

>DURRR BUT IT'S AN INTEGRAL WITH RESPECT TO A VARIABLE DENOTED BY S
Fucking moron.

>>9415072
Ok now Im getting pissed off. Its been quite a few years since I graduated but I still know at least some of my shit even though I never use it because its fucking useless.

When you look at the wiki page. LITERALLY THE FIRST FUCKING EQUATION THAT COMES UP IS THE 2nd FUCKING EQUATION IN THAT FAGGOT TEXT BOOK PAGE.

Now go fucking fuck yourself you god damn autistic larping douche faggot.

>>9415072
ok nevermind. I was wrong...

Gonna print this out and jerk off onto it. God I love owning brainlets.

>>9415102
should probably add this line to your screen shot for authenticity.

>>9414931
Not OP but as someone who took Differential Equations in their first semester of uni, I would not have been able to understand this book. I don't think my class was assigned a text but I used Zill and that was good enough for me.
Just like anything, notation is only good in moderation.

>>9415088
>>9415093
p embarrassing, bro

>>9415138
At least he's not doubling down like some /pol/tard refusing to accept reality.

>>9415138
ya...

Whatever.

So use theorem to solve dy/dx +x^2 +y = C

>>9414944
>>9414921
>>9415007
>>9415021
Here are your (you)'s

stop larping

>>9415163
> = C
Why the long face? You from /r9k/?

>>9415156
some times you gotta throw potential crap out there just to confirm you are not god.

A few weeks ago there was another thread about laplace transforms I posted in. Not sure why I failed this time.

>>9415168
Just solve the fucking differential equation you piece of shit.

>>9414912
>>9415125
The first sentence assumes you have basic knowledge of DEs. The book's obviously not meant to be an introduction.
>>9414953
That book is freely available on archive.org, so it's not hard to check that you're lying.

>>9415171
[math]-e^{-x}((x^2-2x+2)e^{x}-K-Ce^{x})[/math], where [math]K[/math] is a constant that may be satisfied by an initial condition.

>>9415179
>you're lying.
Wrong.

>>9415184
>proceeds to produce absolutely no evidence of not lying
k

>>9415180
meh, bad example.

You don't need the theorem for that one. I could solve it.

Fucking annoying cuz I used to know this shit. And I dont have access to my notes right now.

http://www.jirka.org/diffyqs/
This was the book our class used.
It was easy to read

>>9415193
ahhh I guess maybe you do...

I cant do this right now.

>>9415192
It's the first page of the book, you can download a copy of it yourself from libgen and see, what more proof do you need? Post this supposed archive link so I can laugh at how you don't know how to read

>>9415184
https://archive.org/details/TenenbaumAndPollardOrdinaryDifferentialEquations
>Chapter 1
>Basic Concepts
>How Differential Equations Originate

>>9415195
you set s = x^2 and integrate s+y wrt s right? then integrate, and sub x back in.

ya...

>>9415195
you set s = x^2 ubstitute then integrate both sides wrt to dy and ds. then sub back in.

I think

>>9415195
No, I believe you don't need any theorems. I don't know anything fancy schmancy I just slapped some methods of undetermined coefficients on there. I'd also stay away from notes the most you can and really internalize everything.
As the (un-sourced, probably) Richard Feynman quote goes: "If you can't create it, then you truly don't understand it."
>>9415196
I'm not the guy you think you're replying to. I simply just pointed out that you didn't provide any evidence to the guy who said you're lying. Link me the exact PDF you have and I will download it and either confirm or deny if you really want.

>>9414953
>"Ordinary Differential Equations" by Tenenbaum & Pollard

No
>https://www.math.brown.edu/~mgulian/morris-tenenbaum-harry-pollard-ordinary-differential-equations-copy.pdf

>>9414998
I slipped back to Mt. Stupid over the years.

But thanks to you fuckers I have recovered back to valley of despair.

>>9415211
I did some digging around and I don't know what I used but it is definitely not the method of undetermined coefficients. If it helps to find the method, I did no integrations.

>>9415220
Im pretty sure that theorem in OP is what you use, or at least it makes it easier.

>>9415220
but wtf do I know...

>>9415224
Bro I literally solved it though, see (>>9415180). I used a system of guessing you can call it. Bring the x^2 over to the side with C and make a homogeneous solution and then a particular solution based on -x^2 plus the C. This may be method of undetermined coefficients but the examples I saw online look nothing how I do it.
>>9415226
I don't think it's about what you know, anon. It's about what you can and are willing to learn.

>>9415232
thanks. I can't really see how you solved it that way, so now I am going to have to go through all my notes again because this is really bugging me.

>>9415232
>Bring the x^2 over to the side with C

then just integrate wrt x and you're done. no theorem required.

freagin hell.

>>9415241
or not...

k im done.

>>9415232
>>9415196
>>9414921
Also, I found the book. It is here: http://epubs.siam.org/doi/book/10.1137/1.9780898719222
ISBN: 978-0-89871-510-1
You got the wrong book, OP.

>>9415238
As a linear differential equation, it obeys superposition such that the general solution to the differential equation is the sum of its homogeneous solution and its particular solution.
Solve the homo. solution [math]y'=y[/math]
Then the particular solution you need to guess a form [math]Ax^2+Bx+D[/math] (we already have C, so I picked D) that also obeys [math]y'+y=C-x^2[/math]. Differentiate your particular solution guess and solve for the coefficients. Note that if you have a particular solution that represents your homo. solution, you need to multiply it by a single dimension of the independent variable of y at a time until it no longer represents the homo. solution.

>>9415254
Part of me also really wants to say that this is possible using an integrating factor. Maybe even Laplace Transforms if you're a masochist.

>>9415258
For Laplace Transforms attempts
http://inside.mines.edu/~jcollis/LAPLACE.pdf

>>9415254
that sounds very familiar.

but what is OPs theorem for? it seems familiar too.

>>9415268
Laplace transforms were brutal... that much I remember.

>>9415284
I think it is just establishing ground that a solvable differential equation must have some anti-derivative to it (without having anything whose derivative can satisfy the equation means the equation has no solution).
I'm not a mathematician though, so I can't be too sure this is what it's saying.

>>9415254
Just noticed a mistake. Should be [math]y'=-y[/math] instead of [math]y'=y[/math]. Sorry about that.

>>9415296
maybe Im off base.

I was thinking something along the lines of ODE version of integration by parts

>>9415302
Integration by parts is just a method or technique of solving an integral, and the equation given is just an integral in general. This may or may not include integration by parts, depending on the functions.

>>9415312
Ya, I know that much at least. Still I think OP's theorem is more practical than you're suggesting here
l>>9415296

>>9415312
>>9415302
For a more thought out reply, I think it has more to do with the fundamental theorem of calculus. The text states that "it is clear that [math]y(t)[/math] then has a continuous derivative", supporting the previous claim about the differential equation needing to have this integral equation to represent it since, upon differentiating, the integral changes to the function f(t,y) and y(t) of course goes to y'(t) and the constant y naught goes to zero, which matches (1.1) .

>>9414921
>>9414949
>>9414953
>>9415003
>>9415026
>>9415179
>>9415212
>>9415243
OP here, yeah my bad, I downloaded a PDF that said it was the book but it was actually some other one. the actual book is very good
>>9415184
>>9415192
>>9415179
I love how you accuse me of lying as if I intentionally posted the wrong book and claimed it was another, kek. why would you lie about something you can check in 2 seconds?

>>9415870
>why would you lie about something you can check in 2 seconds?
People lie about stupid shit over the internet all the time, anon.
Also, the /sci/ wiki links are usually pretty good. I personally used Zill and Paul's Online Math Notes and aced the fuck out of my class.

>>9414912
I don't like the font. Apart from that it's fine. Can someone explain to me, why do most maths books have shit fonts ?

how come you guys all suck the other guy's dick but not mine?

>>9416529
i had to bitch at someone today because they were using RK4 in a scenario where RK4 was a poor choice of numerical quadrature method. i still feel bad about it

>>9416516
Probably being stuck in academia for so long made them blind to what anything not-shitty looks like. Or the text was written through a free-to-use LaTeX site which didn't allow other fonts.

>>9414990
Yeah, but it seems that this kind of "jerking off" is the fun part when writing math books.